Parameter Generation Device, System, Method, and Program

The present invention relates to a parameter generation device, a parameter generation system, a parameter generation method, and a parameter generation program for generating desired a parameter.

In research site for new item exploration, huge combinations of factors such as item type, amount, processing temperature, pressure, and time are tried to discover production methods that yield desired performance in new materials. However, the number of these combinations is astronomically large, making it impossible to try all of them.

Generally, from past experiences and simulation results, knowledge has been accumulated on combinations of conditions that can be expected to produce good results and vice versa. Therefore, in research site, the work of determining new combinations of factors within the range that satisfies the conditions indicated by this accumulated knowledge, and verifying the results through prototyping, simulations, etc., is repeated.

In addition, in order to derive a combination of factors that satisfies desired conditions, a mathematical programming solver may be used to derive an optimal combination based on an objective function designed by an engineer or the like and constraint conditions that define the conditions to be satisfied (i.e., a mathematical optimization problem).

Patent Literature 1 describes a design support system that reduces the number of times numerical simulations are performed in examining design parameters for achieving a design target. The design support system described in Patent Literature 1 performs sensitivity analysis to the design target by performing forward analysis given the initial set values of design parameters and then performing inverse analysis based on the results of the analysis based on the accompanying numerical analysis.

In considering a method for producing the desired new item, it is necessary to create a combination of factors for the production of the new item. One such method is to rely on the experience and intuition of skilled personnel. However, this method is highly dependent on individuals, and there is a problem of being unable to carry out work efficiently without specific skilled personnel.

As another method for creating a combination of factors, a method of selecting a combination that satisfies a condition from among combinations of factors selected randomly can be considered. However, as the conditions become more complex, the probability of a combination of factors that satisfies the conditions decreases, resulting in poor efficiency.

On the other hand, it is possible to derive an optimal solution for a designed mathematical optimization problem by using a mathematical programming solver. However, the optimal solution obtained is one for the designed objective function. Usually, in situations where new items are being explored, some combination of types is needed as a candidate for the factors to product the item. Therefore, it is also inefficient for engineers to design a mathematical optimization problem each time a combination of factors is derived.

Additionally, the method described in Patent Literature 1 aims to reduce the number of simulations when considering design parameters to achieve design target and does not derive multiple combinations of factors.

Furthermore, there are cases where the objective function designed by engineers, etc. may not be entirely accurate. In such cases, there is also the problem that the obtained optimal solution may not necessarily be the solution for producing the desired item. Therefore, it is desirable to be able to efficiently discover multiple methods for producing desired items.

The purpose of this invention is to provide a parameter generation device, a parameter generation system, a parameter generation method, and a parameter generation program that can discover multiple methods for producing the desired item.

The parameter generation device according to the present invention includes an input means which accepts input of a first objective function and a constraint condition defining a combination of factors related to item production, an objective function generation means which generates a second objective function by applying stochastic fluctuation to a parameter of the first objective function, an optimization processing means which performs optimization of a model including the second objective function and the constraint condition, and an output means which outputs a value of a variable of the second objective function obtained by the optimization as a parameter set.

The parameter generation system according to the present invention includes a predictive model generation device which uses past experimental data as training data to learn a predictive model with material as explanatory variable and characteristic value indicating a property of an item as objective variable, a first objective function generation device which generates a first objective function defining a combination of factors related to item production using the predictive model, and a parameter generation device which generates a parameter set using the first objective function, wherein the first objective function generation device generates the first objective function, including a linear sum of the characteristic value indicated by the objective variable as a combination of factors, and inputs it into the parameter generation device, and the parameter generation device includes: an input means which accepts input of the first objective function and a constraint condition, an objective function generation means which generates a second objective function by applying stochastic fluctuation to a parameter of the first objective function, an optimization processing means which performs optimization of a model including the second objective function and the constraint condition, and an output means which outputs a value of a variable of the second objective function obtained by the optimization as a parameter set.

The parameter generation method by a computer according to the present invention includes: accepting input of a first objective function and a constraint condition defining a combination of factors related to item production: generating a second objective function by applying stochastic fluctuation to a parameter of the first objective function; performing optimization of a model including the second objective function and the constraint condition; and outputting a value of a variable of the second objective function obtained by the optimization as a parameter set.

The parameter generation program according to the present invention causes a computer to execute: an input process for accepting input of a first objective function and a constraint condition defining a combination of factors related to item production, an objective function generation process for generating a second objective function by applying stochastic fluctuation to a parameter of the first objective function, an optimization processing process for performing optimization of a model including the second objective function and the constraint condition, and an output process for outputting a value of a variable of the second objective function obtained by the optimization as a parameter set.

According to the present invention, it becomes possible to discover multiple methods for producing the desired item.

Hereinafter, example embodiments of the present invention will be described with reference to the drawings.

is a block diagram showing an example of the configuration of an example embodiment of a simulation system of the present invention. The simulation systemof the present example embodiment includes a predictive model generation device, a first objective function generation device, a parameter generation device, an optimization processing device, and a simulator.

The predictive model generation deviceis a device that generates a predictive model that predicts the impact of the type and amount of materials on the characteristics of a product (e.g., items) based on past experimental data. Specifically, the predictive model generation devicelearns a predictive model that predicts value indicating item characteristics (hereinafter referred to as “characteristic value”) based on past experimental data. The characteristic value may also be referred to as performance indicator.

The predictive model generation deviceincludes a storage unit, a learning unit, and a model output unit.

The storage unitstores training data used by the learning unitfor learning. The training data, for example, is data that corresponds to multiple materials used in the production of an item and property values that indicate the item's characteristics such as hardness, toughness, and heat resistance when those materials are used. The storage unitmay be realized, for example, by a magnetic disk, etc.

The learning unitlearns a predictive model with material as explanatory variable and characteristic value as objective variable using past experimental data as training data. The method by which the learning unitlearns the predictive model is arbitrary and may use any method, such as machine learning.

The model output unitoutputs the predictive model generated by the learning unit. The model output unitmay input the predictive model into the first objective function generation device.

The first objective function generation devicegenerates an objective function that defines a combination of factors related to item production to achieve target characteristic values. Here, the factors related to the item production mean the contents to be specified in the production method of the item, and specifically, they mean the type and amount of materials, processing temperature, pressure, processing time, etc. The objective function is defined using parameters such as weights (coefficients) and biases set for each factor.

In other words, the first objective function generation devicegenerates an objective function (hereinafter referred to as the first objective function) used to derive the optimal combination of material type, amount, processing method, etc. that achieves the target value, using the factors related to the production of the item and the parameters described above.

The first objective function generation devicemay generate the first objective function using the predictive model generated by the learning unit. For example, it is assumed that the predictive model for predicting the i-th characteristic value yis expressed as a linear sum of j factors x, as shown in Equation 1 below; as a combination of factors. Here, x-bar (x with an overline) is the average value of the factors, and σ is the standard deviation of the factors, which are calculated when generating the predictive model.

In this case, the first objective function generation devicemay generate the first objective function that includes the linear sum of each characteristic value y. For example, when the weight for each characteristic value yis W, the first objective function generation devicemay generate the first objective function as shown in Equation 2 below. Equation 2 represents the squared linear sum of the deviations from the target median value of the characteristic values. Here, Lmedis the target median value of the characteristic value y. Additionally, Weight Wis determined by engineers, etc. The specification of Wmay be accepted by the first objective function generation deviceor by the parameter generation devicedescribed later.

Furthermore, as shown in Equation 3 below, the first objective function may be expressed in the form of an expansion of Equation 2 above.

In the examples from Equations 1 to 3 above, a, b, Lmed, W, Q, and Lare the parameters described above. In other words, the parameters in this example embodiment include not only the parameters at the time of formulation, but also the parameters obtained during the formulation process.

In the above explanation, the first objective function is configured as a squared linear sum of the deviations from the target median value of the objective variables (characteristic values), but the content included in the first objective function is not limited to characteristic values. The first objective function may include factors other than characteristic values (e.g., processing methods). The first objective function generation deviceinputs the generated first objective function into the parameter generation device.

In this example embodiment, a case in which the first objective function generation deviceis realized as an independent device is illustrated. However, the first objective function generation devicemay be realized integrally with another device, and may be included in the parameter generation device, for example.

The parameter generation deviceis a device that generates a parameter to be input into the simulatorand is connected to the optimization processing deviceand the simulator. The simulatoris a device that performs trials based on the generated parameters. The aspect of the simulatoris arbitrary and may be implemented using known devices.

The optimization processing deviceis a device that performs optimization processing based on the model generated by the parameter generation device. The optimization processing devicemay be realized by a (classical) computer that executes a mathematical programming solver. Alternatively: the optimization processing devicemay be a dedicated device that finds the ground state of the Hamiltonian of an Ising model. In this case, the optimization processing deviceis realized as a device that executes annealing based on the Ising model generated by the parameter generation device.

The parameter generation deviceincludes an input unit, an objective function generation unit, an optimization processing unit, and an output unit.

The input unitaccepts input of the first objective function mentioned above. The input unitalso accepts input of constraint conditions indicating constraints that each factor must satisfy and constraints when combining factors. The input unitmay accept the first objective function generated by the first objective function generation device, or it may accept the first objective function generated manually by other devices (not shown) or engineers, etc.

For example, constraint conditions for producing new items include specifications regarding the selection of material types (one from each material group, etc.), specifications regarding the distribution of material quantities (specifying the sum of the quantities of some materials, specifying the quantities of individual materials, etc.), and specifications regarding exclusive materials. Other constraint conditions on the production of new items may include specifications for processing the material (depending on the material, there are restrictions on the processing temperature (upper limit temperature, etc.) and pressure, etc.).

The objective function generation unitgenerates an objective function (hereinafter referred to as the second objective function) by applying stochastic fluctuations to the parameters of the input first objective function. Here, applying fluctuations to the parameters means performing calculation processing such as addition, subtraction, multiplication, or division on the values indicated by the fluctuations in parameters. The objects for which fluctuations are set include parameters that appear in the final first objective function (e.g., Q, Lin the above Equation 3) as well as parameters that are in the process of being formulated (e.g., a, Lmedin the above Equation 1).

The parameters to which fluctuations are applied are specified in advance. The specification method is arbitrary, and, for example, the input unitmay accept input from engineers, etc., for specifying the parameters to which fluctuations are applied. The fluctuations are applied to the parameters of the objective function, not the constraint conditions.

Specifically, the objective function generation unitapplies fluctuations represented by random variables following a predetermined probability distribution to the parameters of the first objective function. Preferably, the objective function generation unitapplies fluctuations represented by random variables following a probability distribution with mean zero to the parameters of the first objective function. Examples of probability distributions with mean zero include a normal distribution as exemplified by the following Equation 4 and a uniform distribution as exemplified by Equation 5.

To set the average of the probability distribution to zero, in the normal distribution of Equation 4, it may be set μ=0, and in the uniform distribution of Equation 5, it may be set a=−b (b>0). In the case of the normal distribution, the standard deviation o is an indicator of the magnitude of the fluctuation. In the case of the uniform distribution, the width of the interval b-a is an indicator of the magnitude of the fluctuation. In other words, the larger this parameter, the greater the fluctuation, and conversely, the smaller this parameter, the smaller the fluctuation. The similarity to the original objective function (optimization problem) also changes depending on the magnitude of the fluctuation applied.

The following describes how fluctuations, represented by random variables that follow the probability distribution shown in Equation 4 or Equation 5, as illustrated above, are applied to the parameters of the first objective function with reference to Equations 1 to 3 above. The fluctuation applied in this example embodiment is expressed as the equation of a random variable x following the fluctuation probability distribution p(x).

For example, it is assumed that the probability distribution p(X) of the fluctuation is represented by the normal distribution shown in Equation 4 above. In this case, the second objective function obtained by applying the fluctuation Xto Equation 1 above is represented by Equation 6 below: As shown in Equation 6, the standard deviation o is set, for example, to a constant c times the parameter a.

In Equation 6, the indicator of the magnitude of the fluctuation is the standard deviation σ of p(X). Increasing the positive constant c makes it easier to increase the magnitude of fluctuations (i.e., Xtends to increase).

Similarly, the second objective function obtained by applying the fluctuation Xto Equation 2 above is represented by Equation 7 below. As shown in Equation 7, the indicator of the magnitude of the fluctuation is set, for example, to a constant c times the parameter Lmed.